Twin Bites flat cooldown reduction is not effective against structures.

The only exception to Dragon FormTwin Bite applying on-hit effects to all affected targets is Tiamat and Ravenous Hydra's passive effect Cleave, as it has an internal cooldown of 0.05 seconds when triggered on different targets. This is a special case to prevent abuse.

Active:Shyvana surrounds herself in flame for 3 seconds, dealing magic damage to nearby enemies each second, increased by 20% against monsters, and gaining bonus movement speed which decays by 15% of its original value each second.